Achieving Hierarchy-Free Approximation for Bilevel Programs with Equilibrium Constraints
Authors: Jiayang Li, Jing Yu, Boyi Liu, Yu Nie, Zhaoran Wang
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Eventually, the analytical insights are highlighted through numerical examples. Section 6 presents numerical results. Table 1. Firm A s profit in T-step Cournot duopoly and T-step monopoly models with different Ts. Figure 1. Comparison between Algorithm 1 and 2 starting from different initial points. Figure 2. Comparison between fixedand adaptive-initialization strategies (Algorithm 3). Figure 4. Comparison between our methods and previous methods. |
| Researcher Affiliation | Academia | 1Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL, USA 2Department of Industrial Engineering and Management Science Engineering, Northwestern University, Evanston, IL, USA. Correspondence to: Yu (Marco) Nie <y-nie@northwestern.edu>. |
| Pseudocode | Yes | Algorithm 1 Solving T-step Cournot game. Algorithm 2 Solving T-step monopoly model. Algorithm 3 Adaptive-initialization strategy for approximating Problem (1). |
| Open Source Code | No | The paper does not explicitly provide a link to its own source code for the methodology or state that the code is publicly released. |
| Open Datasets | Yes | The network data (topology, travel demand, arc travel time function) are downloaded from the Transportation Network Git Hub repository1. 1https://github.com/bstabler/Transportation Networks/tree/master/Sioux Falls |
| Dataset Splits | No | The paper does not provide specific details about training/validation/test dataset splits for its experiments. |
| Hardware Specification | Yes | total CPU (2.9 GHz Quad-Core Intel Core i7) time |
| Software Dependencies | No | The paper mentions software like TensorFlow, PyTorch, and cvxpylayers with citations (e.g., 'Abadi, M. et al., 2016' for TensorFlow, 'Paszke, A. et al., 2019' for PyTorch, and 'Agrawal, A. et al., 2019' for cvxpylayers), but does not explicitly state specific version numbers for these software components or other dependencies. |
| Experiment Setup | Yes | We set m(x) = w, x2 , d = 6, u0 = [1, 3, 3, 0.5, 1]T, v0 = [2, 4, 4, 1, 2]T, w = [1, 3, 3, 0.5, 1]T, and γ = 1. with r = 0.4 and T = 0, . . . , 4. At each round, x0 is randomly sampled from a Gaussian distribution while y0 is first randomly sampled from a uniform distribution and then re-weighted to fit the constraint. Fixed initialization strategy: we follow the procedure devised at the end of Section 5.2; the initial solutions are set as x0 = [0, 0, 0, 0]T and y0 = [0.4, 0.3, 0.2, 0.1] whenever Algorithms 1 and 2 are invoked. the learning rate r, which is set to be 0.1 in the projection-method version and 0.25 in the mirror-descent version. |